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Follow instructions to fold sheets of A4 paper into pentagons and assemble them to form a dodecahedron. Calculate the error in the angle of the not perfectly regular pentagons you make.

Platonic Planet

Stage: 4 Challenge Level:

How much of the planet's surface can the alien see if she is in the
middle of one of the faces?
What about on one of the edges?
Or at a vertex?

Try to picture a route around the planet either in three dimensions
or on a net. Can you be sure every point on the surface is visible
from your route? Can you make a more efficient route? Some diagrams
might help!

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities
can be found here.